A master-surface to master-surface formulation for beam to beam contact

Part I: Frictionless interaction

authored by: Alfredo Gay Neto, Paulo M. Pimenta, Peter Wriggers
Abstract: In this paper a surface to surface frictionless contact formulation is presented, which is appropriate to the analysis of beam to beam contact. Parameterized surfaces are assumed to represent the boundaries of the bodies that are candidate to contact. The material points of each surface are described using convective coordinates. No master-slave distinctions are made, once both bodies are parameterized and no slave points are elected. We assume a single point contact interaction, in which the contact point can move along different material points of the surfaces. On the other hand, these surfaces can change since the bodies experience large deformation. To determine the candidate material points to contact, we solve the minimum distance problem between the two surfaces. The equations for obtaining the mechanical contact interaction and the consistent linearization are herewith derived. The proposed formulation can be applied disregarding the nature of the model degrees of freedom. Subsequently one has established the surface parameterizations, the contact formulation can be directly used. As an illustration of the power of our formulation, we present an application for beams with superelliptical cross sections.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Universidade de Sao Paulo
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 303
Pages: 400-429
No. of pages: 30
ISSN: 0045-7825
Publication date: 01.05.2016
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2016.02.005 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{47953f7e6b0b4cc6a90760d34aa0454c,
title = "A master-surface to master-surface formulation for beam to beam contact: Part I: Frictionless interaction",
abstract = "In this paper a surface to surface frictionless contact formulation is presented, which is appropriate to the analysis of beam to beam contact. Parameterized surfaces are assumed to represent the boundaries of the bodies that are candidate to contact. The material points of each surface are described using convective coordinates. No master-slave distinctions are made, once both bodies are parameterized and no slave points are elected. We assume a single point contact interaction, in which the contact point can move along different material points of the surfaces. On the other hand, these surfaces can change since the bodies experience large deformation. To determine the candidate material points to contact, we solve the minimum distance problem between the two surfaces. The equations for obtaining the mechanical contact interaction and the consistent linearization are herewith derived. The proposed formulation can be applied disregarding the nature of the model degrees of freedom. Subsequently one has established the surface parameterizations, the contact formulation can be directly used. As an illustration of the power of our formulation, we present an application for beams with superelliptical cross sections.",
keywords = "Beam, Contact, Superellipse, Surface-to-surface",
author = "{Gay Neto}, Alfredo and Pimenta, {Paulo M.} and Peter Wriggers",
note = "Funding Information: The first author acknowledges FAPESP (Funda{\c c}{\~a}o de Amparo {\`a} Pesquisa do Estado de S{\~a}o Paulo) for the support under the grant 2014/17701-4 . The second author expresses his acknowledgement to CNPq (Conselho Nacional de Desenvolvimento Cient{\'i}fico e Tecnol{\'o}gico) under the grant 303091/2013-4 , as well as the Alexander von Humboldt Foundation for the Georg Forster Award that made possible his stay at the Universities of Duisburg–Essen and Hannover in Germany as well as to the French and Brazilian Governments for the Chair CAPES-Sorbonne that made possible his stay at Sorbonne Universit{\'e}s (UTC) on a leave from the University of S{\~a}o Paulo.",
year = "2016",
month = may,
day = "1",
doi = "10.1016/j.cma.2016.02.005",
language = "English",
volume = "303",
pages = "400--429",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}